This document describes the LZW compression algorithm. It is a dictionary-based algorithm that is lossless and commonly used to compress image files and in the Unix 'compress' command. The algorithm works by building a dictionary of strings as it encodes the data, replacing repeated strings with codes. When decoding, the same dictionary is rebuilt to map codes back to strings. An example shows how a short string is compressed from 80 bits to 63 bits using LZW encoding by extending the symbol size from 8 to 9 bits.

1. LZW Compression Algorithm
Presented by : keyvan moazami
Multimedia course
Shamsipour college
Spring 2015

2. Probability base algorithms problems
 First approach
 analyze a few books and estimate the probabilities of different letters
 Then apply Huffman coding
o probability depend on context
 Adaptive encoding
 two pass process
 Huffman code customized (letter and group letter)
o strategy is expensive but workable
o symbol grouping (larger or smaller)
o We need different approach for adaptive algorithm
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3. Lempel-Ziv-Welch (LZW) algorithm
 Dictionary base
 Used to compress image file , Unix ‘compress’ command , …
 Lossless
 * Dictionary table never transmitted
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4. How work LZW
 Example : ASCII code.
 Typically, every character is stored with 8 binary bits, allowing up to 256 unique
symbols for the data .
 This algorithm tries to extend this library to 9 to 12 bits per character. The new
unique symbols are made up of combinations of symbols that occurred
previously in the string.
 Does not always compress well , especially with short, diverse strings. But is good
for compressing redundant data, and does not have to save the new dictionary
with the data :this method can both compress and uncompressing data .
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5. Example :
 I want to compress the following string :
Thisisthe
By default using uncompressed ASCII , this is equal to
01110100011010000110100101110011011010010111001101110100011010000110010101110011
Or
116 104 105 115 105 115 116 104 101 115
* That’s 80 bits. We can do better
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6. Example : LZW Algorithm
 I want to compress the following string :
Thisisthe
 Start adding pairs of symbols to dictionary of words .
 When we reach a pair that we’ve already placed in the dictionary ,
replace that pair with our new dictionary value.
For this tiny string , we will only need 9-bits , allowing up to 512 unique symbols .
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8. Example : LZW Algorithm
 I want to compress the following string :
Thisisthe
current next output Add to dictionary
t 116 h 104 t 116 th 256
h 104 i 105 h 104 hi 257
i 105 s 115 i 105 is 258
s 115 i 105 s 115 si 259
i 105 s 115 ‘is’ is in the dictionary ! Check if ‘ist’ is
is 258 t 116 is 258 ist 260
t 116 h 104 ‘th’ is in the dictionary ! Check if ‘the’ is
th 256 e 101 th 256 the 261
e 101 - e 101 -
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9. Example : LZW Algorithm
 I want to compress the following string :
Thisisthe
current next output Add to dictionary
t 116 h 104 t 116 th 256
h 104 i 105 h 104 hi 257
i 105 s 115 i 105 is 258
s 115 i 105 s 115 si 259
i 105 s 115 ‘is’ is in the dictionary ! Check if ‘ist’ is
is 258 t 116 is 258 ist 260
t 116 h 104 ‘th’ is in the dictionary ! Check if ‘the’ is
th 256 e 101 th 256 the 261
e 101 - e 101 -
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10. Example : LZW Algorithm
 I want to compress the following string :
Thisisthe
116 104 105 115 258 256 101
Or
001110100 001101000 001101001 001110011 100000010 100000000 001100101
Notice that our symbols are now made up of 9 bits each instead of 8 .
This is 63 bits long , instead of the original 80 bits.
That’s 78.75 % of what it used to be !
Dictionary table not Save !
How decompress data ?
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11. Uncompressing:
 To uncompressing ,we do need to know how many bits were used in the
compression, the one new information that is kept with the data when
saved to a file (else, the number of bits is specified by a program or a user).
 We can read in the characters and build the new dictionary the same way
as we did for compressing .When we reach a symbol outside the ASCII
range (>255},then we should have that value ready to be seen in the
dictionary.
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12. Example : decompressing LZW
 I want to decompress the following string :
116 104 105 115 258 256 101
current next output Add to dictionary
116 104 116 116 104 (256)
104 105 104 104 105 (257)
105 115 105 105 115 (258)
115 258 115 115 105 115 (259)
258 256 105 115 105 115 116 (260)
256 101 116 104 116 104 101 (261)
101 - 101 -
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13. Example : decompressing LZW
 I want to decompress the following string :
116 104 105 115 258 256 101
current next output Add to dictionary
116 104 116 116 104 (256)
104 105 104 104 105 (257)
105 115 105 105 115 (258)
115 258 115 115 105 115 (259)
258 256 105 115 105 115 116 (260)
256 101 116 104 116 104 101 (261)
101 - 101 -
116 104 105 115 105 115 116 104 101
Or “thisisthe”
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14. Example : decompressing LZW
 I want to decompress the following string :
116 104 105 115 258 256 101
115 258 115 115 105 115 (259)
258 256 105 115 105 115 116 (260)
256 101 116 104 116 104 101 (261)
Why didn’t we add 258 256 ( 105 115 116 104 ) to the dictionary at (260) ?
Weird case : remember , dictionary is made with combinations one
character at a time , so you would only add the first symbol of the
combination to the current combination when rebuilding the dictionary .
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15. Thank you